自由境界を有する確率的双曲型方程式の解の安定性と分岐について

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書誌事項

タイトル別名
  • On Stability and Bifurcation of Solutions of Stochastic Hyperbolic Equation with Free Boundary
  • Application to Micro-Tunneling Machine
  • マイクロトンネル機械への応用

抄録

We study a stability property for stochastic hyperbolic equation with free boundary. This model is motivated by a micro-tunneling machine which is used for the conduit installation for communication cables. By using this tunneling machine, a flexible pilot pipe is thrusted into the ground and hence the total length of the inserted pipe becomes a function of time. Furthermore, the thrust force generated by a hydraulic jack is stochastically perturbed. The transverse displacement of the inserted pipe is firstly shown to be governed by a hyperbolic equation with free boundary by using the Hamilton principle. Secondly, the existence of a solution of this equation is proved. For checking the buckling phenomena the stochastic stability is studied. Two digital simulation examples are demonstrated.

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